Having worked oin the finance industry for a number of years, and been impacted by the current credit climate, lenders criteria now is very strict in terms of missed payments on "unsecured", therefore if there are "secured" missed payments and no equity in your property, the likelyhood of obtaining a debt consol loan is very unlikely.
Lenders will veiw a number of things in different ways, however, to a lender debt consol is a "high risk" loan. With missed payments which will be showing, then that pushes the risk even further. Rate is for risk, too much risk and it will decline. Another factor is affordability. Granted you are looking to debt consol, lenders will look at how much you are wanting to borrow, then check affordabilty against an amount that is double. Ie.... You want to consol 10k... Lenders will look to see if you can afford 20k. The reason is people recieve the money in their account then spend it. I'm not saying you would, but a lot have people have done it.
In terms of payments, when a lender looks at you, apart from credit score, the last thing that a person would put at risk is their home in missing payments, therefore to a lender, if you a missing payments on a secured loan that keeps a roof over your head, shows serious financial stress.
You need to speak to the CCCS, they will point you in the right direction, but a consol loan does not sound like an option.